Problems with Developmental MathNationally Lengthy sequence with low pass rates Repeat of high school content Skill-heavy initiatives repackage but do not change contentLocally Successful traditional program but one size fit all Intermediate algebra was not an appropriate prerequisite for all college level courses
Solutions Look forward to courses students will take Update content, balance instruction, diversify assessment Use technology when it is most appropriate Differentiate pathways with new prerequisite courses
A New Course, A Simple GoalIn one semester, Mathematical Literacy forCollege Students gives a student at the beginningalgebra level the mathematical maturity to besuccessful in statistics, liberal arts math, orintermediate algebra.
Initiatives2009 AMATYC New Life initiative begins.2010 New Life leads to Statway and Quantway (formerly Mathway), funded by Carnegie. Carnegie AMATYC2011 19 Carnegie grant schools pilot Quantway New Life Statway.2011 Rock Valley College pilots MLCS. MLCS2012 8 Carnegie grant schools pilot MLCS.
FAQsWhat is the difference between Statway andQuantway?
Take a lookExplore a lesson
DiscoverSomewhere, something incredible iswaiting to be known. - Carl Sagan
Content Philosophy Areas of focus Role of intermediate algebra
A New PerspectiveWe do not act as though these students havenever seen algebra because most have for years.New approach: Emphasis on understanding over manipulation alone Application, connections, retention Evaluation of appropriate methods per the situation Focus on needs of outcome courses, work, life Incorporate needs of other disciplines biology, nursing, chemistry, business
Area 1: NumeracyStart with numbers and Example:understand them. Program cells in Excel toGeneralize when it makes evaluate a formula.sense to.Stay concrete; stay tangible.Goal: Understand thatnumbers are quantities.Emphasize units.
Area 2: Algebraic ReasoningAvoid problems without Example:context whenever possible. Build a cost model for a Kindle and Nook to compare againstUse numeric methods until the cost of a hardcover book.students want and value the When is each worth it? Usealgebraic method. graphs, equations, and tables.Strive for meaningful situations N=179 + 12.99Band variables. K=79 + 12.99BGoal: Judge when algebra H=35Bmakes sense and how to use it.
Area 3: Proportional ReasoningWe work with fractions, Example: Interpret a nutrition label. Userates, and proportions in recommended values for a 2000multiple places in many calorie diet to determine values for a 3000 calorie diet.ways.Goal: Write rates withunits; scale, interpret,and use them.
Area 4: FunctionsWe work on numeracy, Example:algebraic reasoning, and Build a model. Plot points by handproportions all the while or Excel. Determine shape anddeveloping function analyze.understanding. Constant vs. variable Hours to pay for gallon of gas 7 Independent vs. dependent 6 variable 5 Input values that make sense 4 3Goal: Move between tables, 2 1graphs, and equations fluidly. 0 0 10 20 30 40
Additional Embedded AreasGeometry StatisticsMeasurement, units, shapes, simil Centers, variation, correlation, proarity babilityExample: Example:If we overfill a medical measuring Understand variation, build thecup/spoon by 1 mm, which would standard deviation formula, use itproduce a greater overdose error? to find s.d. for a data set, interpretEstimate volume in cc’s and find it in context.actual and percentage change. ( x mean)2 s n 1
Additional Embedded AreasStudent Success Approach to content increases motivation and develops metacognition First week lays foundation for first unit First unit lays foundation for course Lessons address student success while addressing math topics Specific strategies for studying and test taking are taughtMathematical Success Role of accuracy, precision, and error are explored Polya’s problem solving method is used regularly Multiple approaches to problems build understanding Verbal, numeric, algebraic, graphic
Addressing Intermediate Algebra Modeling with non-linear functions (quadratic, exponential, rational, radical) Numerical, graphical, and conceptual understanding is emphasized Emphasis on scatterplots, correlation, and regression De-emphasize worst case algebraic problems in favor of time on other topics*Symbolic manipulation can be addressed in a traditional IA course for STEM-bound students or future bridge course
FAQsWhat about factoring?Does this course “dumb down” developmentalmath standards for entry into college levelcourses?Are you pushing students away from STEM majors?
Development & Instruction Research Content approach Quantway goals Technology
Using Research Researched schools, programs, and countries who are effectively teaching mathematics (not just algebra) Read and incorporated information on how the brain learns
Traditional Approach: Linear Theory, then applications if time Proportions Each strand done Functions separately to Numbers Algebra completion Algebra is primary focus Skill based Examples of every possible variation of skill (problem recognition)
New Approach: Integrated & Layered Applications to motivate, then theory as needed Proportional Reasoning Reasoning Numeracy Functions Algebraic Strands addressed each unit in an integrated fashion going deeper each time Equal time on each strand Concepts-based Fewer skills, more connections Undercurrent of geometry, statistics, student success, mathematical success
Technology for the 21st Century Mental arithmetic is encouraged whenever possible. Calculators are used when they are needed. Excel is used for analyzing patterns and making graphs.
Quantway Goals for Instruction Students actively work on richEngagement problems, both closed and open- ended. Instruction is balanced.Connections Students make sense of topics in the given setting and others. Students are allowed to struggle, butProductive persistence assistance is provided when necessary. Students complete homeworkDeliberate practice assignments which forge connections and deepen conceptual understanding.
Strike a Balance: Accessible Challenges Engagement FrustrationNeed enoughstructure togive students Contextual Theoreticalcomfort butnot so much Online HW/Tech Paper HW/By handthat it ismonotonous Group Work Lecture Open-ended Single solution
FAQsIs there any direct instruction?What reaction do you get from students? Do theybuy-in?Will students be able to transition back to atraditional course?
Assessment Homework Unit assessments
HomeworkStructure: Specific and intentional MyMathLab for skill mastery Paper conceptual homework to connect & apply Fewer problems – do them allApproach: Flipping the classroom Use online system for skill development Problem solve in the classroom
Unit AssessmentsRegular assessments Online quiz and paper assessment twice in unit Project completed throughout unit Open-ended problem Tests Maintain MML-type skills accountability Concepts (fill-in-blank) Applications Project-related questions
FAQsCan developmental students completeopen-ended problems?
Take a lookExplore an open-ended project
ConnectSuccess is a science; if you have theconditions, you get the result. - Oscar Wilde
Making MLCS a Reality Lessons from RVC redesign & pilot Implementation ideas Tips for getting started
Using experience to redesign with MLCS Incorporated lessons learned in our redesign Advising Pace A comprehensive approach Materials Continual assessment Training sessions and materials
Lessons from the pilotStudents want to mimic. They resist at first.They have to be taught how to study and succeed inthis type of course, which is like a college level class.Mastery learning in online systems ≠ learning.Context can go a long way in improving connections and understanding.Reflection is necessary to make sense of a lesson in the larger scheme.We cannot help them all, but we can accelerate the process for many.
Implementation IdeasReplace Beginning Algebra STEM Intermediate College Algebra Level MathPrealgebra MLCS Non-STEM College Level Math (Statistics, Libe ral Arts Math)
Implementation IdeasUse MLCS lessons in an emporium for once-weekly problem solving sessions Beginning Intermediate College Prealgebra Algebra Algebra Level Math 0 Previews content for some, connects for others 0 Everyone is engaged 0 More than just skills
Implementation IdeasAugment traditional sequence with MLCSas a non-STEM alternative preparationfor statistics/liberal arts math. STEM Beginning Intermediate College Algebra Algebra Level Math Prealgebra Non-STEM MLCS College Level Math (Statistics, Libe ral Arts Math) Students who change their major can take intermediate algebra as a bridge to STEM courses.
RVC Course Sequence
Getting Started with MLCS Choose materials Create a collaboratory for pilot Sit in on other MLCS classes is possible Meet with other MLCS instructors regularly Test with common instruments Train new faculty Developing training workshops Materials provide great faculty support
FAQsWhat is your placement tool?How many credit hours is the course?Can we omit topics that you may need?
ReflectThe farther backward you canlook, the farther forward you cansee. -Winston Churchill
Lesson and Unit Protocol MOTIVATE: Explore an interesting situation or hook DEVELOP: Learn more about a topic through activities, mini- lecture, hands-on activities, etc. CONNECT: Associate concepts back and forward REFLECT: Wrap-up topic Self-similarity approach PRACTICE: online for skills, paper for concepts & applications
For More InformationKathleen Almy firstname.lastname@example.org http://almydoesmath.blogspot.com Blog contains info from pilot including video Contains info on our school’s redesignHeather Foes email@example.com